What Is Homoskedastic?
Homoskedastic (also spelled “homoscedastic”) refers to a condition in which the variance of the residual, or error term, in a regression model is constant. That is, the error term does not vary much as the value of the predictor variable changes. Another way of saying this is that the variance of the data points is roughly the same for all data points.
This suggests a level of consistency and makes it easier to model and work with the data through regression. A lack of homoskedasticity may suggest that the regression model needs additional predictor variables to explain the performance of the dependent variable.
Key Takeaways
- Homoskedasticity occurs when the variance of the error term in a regression model is constant.
- If the variance of the error term is homoskedastic, the model is well-defined. If there is too much variance, the model may not be defined well.
- Adding additional predictor variables can help explain the performance of the dependent variable.
- Oppositely, heteroskedasticity occurs when the variance of the error term is not constant.
The Importance of Homoskedasticity
Homoskedasticity is one assumption of linear regression modeling, and data of this type works well with the least squares method. If the variance of the errors around the regression line varies much, the regression model may be poorly defined.
Conversely, heteroskedasticity (just as the opposite of “homogenous” is “heterogeneous”) refers to a condition in which the variance of the error term in a regression equation is not constant.
Special Considerations
A simple regression model, or equation, consists of four terms. On the left side is the dependent variable, representing the phenomenon the model seeks to “explain.” On the right side are a constant, a predictor variable, and a residual term, also known as an error term. The error term shows the amount of variability in the dependent variable that is not explained by the predictor variable.
Real-World Example: Homoskedasticity in Student Test Scores
Suppose you wanted to explain student test scores using the amount of time each student spent studying. In this case, the test scores would be the dependent variable and the time spent studying would be the predictor variable.
The error term would show the variance in the test scores not explained by the studying time. If that variance is uniform, or homoskedastic, this suggests the model may adequately explain test performance—that is, the time spent studying explains the test scores.
But the variance may be heteroskedastic. A plot of the error term data may show a large amount of study time corresponded closely with high test scores, but low study time test scores varied widely and even included some very high scores. This indicates the variance of scores was not well-explained by the amount of time studying alone, suggesting other factors are at work. The model would likely need enhancement to identify these factors.
Further investigation may reveal other factors impacting scores, such as:
- Some students had seen the answers to the test ahead of time
- Students who had previously taken a similar test didn’t need to study
- Some students have inherent test-taking skills independent of their study time
To improve the regression model, a researcher may include other explanatory variables that could provide a better fit to the data. For instance, if some students had seen the answers in advance, the regression model would then have two explanatory variables: time studying and prior knowledge of the answers. With these variables, more of the variance in the test scores would be explained, and the variance of the error term might then be homoskedastic, suggesting that the model is well-defined.
Why Is Homoskedasticity Important?
Homoskedasticity is crucial because it ensures the dissimilarities in a population are accurately identified. Any unequal variance in a population or sample can produce skewed or biased results, making the analysis incorrect or worthless.
The Bottom Line
In a linear regression model, homoskedasticity indicates that the variance of the error term is constant, suggesting the model is well-defined. Conversely, too much variance, known as heteroskedasticity, implies other factors influence the dependent variable. These factors need consideration through further investigation or modeling.
Related Terms: Heteroskedasticity, Linear Regression, Error Term, Variance.
